# Function notation

### Function notation

Function notation is another way to express the y value of a function. Therefore, when graphing, we can always label the y-axis as f(x) too. It might look confusing, but let us show you how to deal with it.

#### Lessons

• Introduction
Introduction to function notations
a)
Equations VS. Functions

• 1.
If $f(x) = 5x^2-x+6$ find the following
a)
${f(\heartsuit)}$

b)
${f(\theta)}$

c)
${f(3)}$

d)
${f(-1)}$

e)
${f(3x)}$

f)
${f(-x)}$

g)
${f(3x-4)}$

h)
${3f(x)}$

i)
${f(x)-3}$

• 2.
If f(x) = 6 - 4x, find:
a)
f(3)

b)
f(-8)

c)
f(-2/5)

• 3.
If f(r) = $2\pi r^2h$, find f(x+2)

• 4.
If ${f(x) = \sqrt{x},}$ write the following in terms of the function ${f.}$
a)
${\sqrt{x}+5}$

b)
${\sqrt{x+5}}$

c)
${\sqrt{2x-3}}$

d)
${-8\sqrt{x}}$

e)
${-8\sqrt{2x-3}}$

f)
$4\sqrt{x^{5}+9}-1$

• 5.
If f(x) = -3x + 7, solve for x if f(x) = -15

• 6.
The temperature below the crust of the Earth is given by C(d) = 12d + 30, where C is in Celsius and d is in km.
i.) Find the temperature 15 km below the crust of the Earth.
ii.) What depth has a temperature of $186^\circ$C?